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ASYMPTOTICALLY LINEAR BEAM EQUATION AND REDUCTION METHOD
Choi, Q-Heung,Jung, Tacksun The Kangwon-Kyungki Mathematical Society 2011 한국수학논문집 Vol.19 No.4
We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.
The existence of solutions of a nonlinear wave equation
Choi, Q-Heung,Jung, Tack-Sun Korean Mathematical Society 1996 대한수학회논문집 Vol.11 No.1
In this paper we investigate the existence of solutions of a nonlinear wave equation $u_{tt} - u_{xx} = p(x, t, u)$$ in $H_0$, where $H_0$ is the Hilbert space spanned by eigenfunctions. If p satisfy condition $(p_1) - (p_3)$, this nonlinear gave equation has at least one solution.
APPROXIMATION THEOREMS IN THE THEORY OF PSEUDODIFFERENTIAL OPERATORS
Choi, Q-Heung Korean Mathematical Society 1983 대한수학회보 Vol.20 No.2
In this paper we shall continue the study of the approximation theorems in the double pseudodifferential operators as in the single pseudodifferential operators.
Choi, Q-Heung,Jin, Zheng-Guo Korean Mathematical Society 2000 대한수학회보 Vol.37 No.4
We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.
STABILITY ON SOLUTION OF POPULATION EVOLUTION EQUATIONS WITH APPLICATIONS
Choi, Q-Heung,Jin, Zheng-Guo Korean Mathematical Society 2000 대한수학회논문집 Vol.15 No.4
We prove the non-homogeneous boundary value problem for population evolution equations is well-posed in Sobolev space H(sup)3/2,3/2($\Omega$). It provides a strictly mathematical basis for further research of population control problems.